A simplified wave enhancement criterion for moving extreme events

Abstract

An analytical model is derived to efficiently describe the wave energy distribution along the main transects of a moving extreme weather event. The model essentially builds on a generalization of the self‐similar wave growth model and the assumption of a strongly dominant single spectral mode in a given quadrant of the storm. The criterion to anticipate wave enhancement with the generation of trapped abnormal waves defined as gr/ur2≈cTtrue(ur/Vtrue)1/q, with r, u, and V, radial distance, average sustained wind speed, and translation velocity, respectively. Constants q and cT follow the fetch‐law definitions. If forced during a sufficient time scale interval, also defined from this generalized self‐similar wave growth model, waves can be trapped and large amplification of the wave energy will occur in the front‐right storm quadrant. Remarkably, the group velocity and corresponding wavelength of outrunning wave systems will become wind speed independent and solely related to the translating velocity. The resulting significant wave height also only weakly depends on wind speed, and more strongly on the translation velocity. Compared to altimeter satellite measurements, the proposed analytical solutions for the wave energy distribution demonstrate convincing agreement. As analytically developed, the wave enhancement criterion can provide a rapid evaluation to document the general characteristics of each storm, especially the expected wavefield asymmetry.

Small‐scale open ocean currents have large effects on wind wave heights

“…At shorter scales, the relative wind and advection effects become more important. Previous discussions of H s gradients have emphasized the importance of wind variability [ Abdalla and Cavaleri , ] or nonlinear wave evolution [ Badulin , ; Kudryavtsev et al ., ]. Our results suggest that current effects cannot be ignored at scales shorter than 200 km.…”

A Simplified Model for the Baroclinic and Barotropic Ocean Response to Moving Tropical Cyclones: 2. Model and Simulations

“…To note, the present model setup can also be used to test impacts of asymmetrical wave fields, that is, associated with possible trapping and enhancement of large surface gravity waves in the front‐right storm quadrant (Kudryavtsev et al, ; Young, ). Indeed, wave‐induced mixing, including breaking impacts and the combined action of wave‐induced drift and wind‐induced shear (e.g., Reichl et al, ), certainly contributes to the turbulent kinetic energy (TKE) balance equation.…”

“…The depth, d w ≈ 1/(3 k p ), influenced by surface waves (Babanin & Haus, ) shall thus be related to TC characteristics at previous time steps. Such a nonlocal impact can then be suggested to enter the correcting factor , with a thickness, h 0 = d w , now more directly related to wave parameters, for example, peak frequency/wave number (see, e.g., equations and for trapped waves in Kudryavtsev et al, ).…”

A Simplified Model for the Baroclinic and Barotropic Ocean Response to Moving Tropical Cyclones: 1. Satellite Observations

“…Thanks to multiple satellite remote sensing observations and improved available in situ measurements, the upper ocean responses to moving tropical cyclones (TCs) are today often very well captured and monitored (e.g., Shay, , and references therein). TCs generate a variety of responses: asymmetrical sea states (e.g., Hwang & Fan, ; Kudryavtsev et al, , Wright et al, ), internal motions at superinertial and inertial frequencies (Geisler, ; Gill, ; Longuet‐Higgins, ; Meroni et al, ; Price, ), geostrophically balanced motions, and turbulence, all contributing to irreversible vertical mixing through the combination of surface stirring, shear at the base of the mixed layer, and convective cooling. As results of all these interactions and adjustments, upper ocean responses to extreme wind forcing by moving TCs still remain difficult to fully elucidate.…”

“…Overall, TC-induced ocean cooling has then been reported to be more pronounced when the storm is intense, the mixed layer shallow with a sharp thermocline, and is slowly moving (e.g., D'Asaro et al, 2014;Lin et al, 2009;Mei et al, 2012). For the later conditions, the resulting sea state is more symmetrical, as trapped fetch effect mostly occurs for a fast-moving TC (Kudryavtsev et al, 2015). For slowmoving TCs, the circular wind pattern will further trigger Ekman pumping, driving surface water away from the storm center, with associated isopycnal uplifts that can typically reach 50-100 m (Babin et al, 2004;Walker et al, 2005).…”